1. Field of the Invention
This invention relates to a method and apparatus of determining the stator flux estimate of an electric machine, comprising the determination of
a stator current taken by the electric machine;
a voltage supplied to the stator of the electric machine,
a stator resistance estimate of the electric machine; and
a stator flux estimate of the electric machine as a time integral of the difference between the voltage supplied to the stator and the product of the stator current and the stator resistance estimate, whereby the stator resistance estimate of the electric machine is determined by correcting the initial value or another earlier value of the stator resistance on the basis of the stator current component parallel to the stator flux estimate, the air gap flux, estimate or the rotor flux estimate.
Related art As is known, the flux produced in the stator windings of an electric machine can be determined by calculating the time integral of the voltage supplied to the stator windings. However, the voltage causing the flux is not directly the voltage u.sub.s supplied to the poles of the winding but a voltage e.sub.s obtained by subtracting the resistive voltage drop R.sub.s . i.sub.s of the stator from the voltage u.sub.s. EQU e.sub.s =u.sub.s -R.sub.s . i.sub.s ( 1)
When determining the flux of the stator side, the proportion of the voltage developing the flux and the voltage drop to the supply voltage has to be known. As the stator current is measured, and the voltage is the product of the current and the resistance according to Ohm's law, the only remaining unknown parameter is the resistance of the stator circuit. The estimated stator flux is thus obtained from the formula ##EQU1## where .PHI..sub.sest =the estimated stator flux
u.sub.s =the stator voltage PA1 i.sub.s =the stator current PA1 R.sub.sest =the estimated stator resistance PA1 T=the electric torque caused by the machine PA1 k.sub.1 =a constant coefficient PA1 .PHI..sub.s =the stator flux PA1 i.sub.s =the stator current
When the electric machine is operated in the constant flux range, the basic frequency w.sub.s of the machine is substantially directly proportional to the supply voltage u.sub.s. The effective value of the voltage is therefore low at low frequencies and high at high frequencies. Since the voltage drop, however, is not dependent on the frequency but merely on the stator resistance and current, the proportion of the voltage drop to the supply voltage increases with decreasing supply frequency. As a result, the influence of the stator resistance is very significant at low frequencies and therefore it is necessary to know its value the more accurately the lower the voltage supplied to the machine is.
The torque developed by the electric machine is determined by the cross product of the flux and the current. Utilizing the stator flux and stator current, the torque can be represented in the form EQU T=k.sub.1 . .PHI..sub.s .times.i.sub.s ( 3)
where
Equivalently, the torque estimate T.sub.est of the machine is obtained by utilizing the estimated flux .PHI..sub.sest and the stator current i.sub.s. EQU T.sub.est =k.sub.1 . .PHI..sub.sest .times.i.sub.s ( 4)
The vector diagram of FIG. 1 of the attached drawings illustrates the influence of an error occurring in the value of the stator resistance estimate R.sub.sest on the estimate T.sub.est of the torque developed by the electric machine. If the estimated stator resistance R.sub.sest of Formula (1) is smaller than an actual value R.sub.s, the angle between the actual stator current i.sub.s and stator flux .PHI..sub.s is smaller than the angle between the stator current and the estimated stator flux .PHI..sub.sest, whereby the actual developed torque is smaller than the torque T.sub.est calculated by the control system. As a result, the electric machine does not develop the desired torque. The smaller the supply voltage, the greater the difference between the calculated and the actual value of the torque will be.
Previously, there has not been any efficient method by means of which the stator flux of an electric machine could be estimated appropriately even at a low supply voltage, taking into account the stator resistance and its changes merely by means of an estimating method based on the measurement of the stator current and stator voltage.